arXiv:1611.04873 · Physical review. B./Physical review. B

Numerical study of magnetization plateaus in the spin- 1 2 Heisenberg antiferromagnet on the checkerboard lattice

Sylvain Capponi

Published Jan 18, 2017• 16 citations

Abstract

We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaus for $m=0, 1/4, 1/2$, and $3/4$, where $m$ is the magnetization normalized by its saturation value. These incompressible states correspond to somewhat similar valence-bond crystal phases that break lattice symmetries, though they are different from the already established plaquette phase for $m=0$. Our results are based on exact diagonalization as well as density-matrix renormalization-group large-scale simulations and interpreted in terms of simple parameter-free trial wave functions.

DOI: 10.1103/physrevb.95.014420

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Multiple magnetization plateaus and magnetic structures in the S = 1 2 Heisenberg model on the checkerboard lattice

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arXiv:1611.04873 · Physical review. B./Physical review. B

Numerical study of magnetization plateaus in the spin- 1 2 Heisenberg antiferromagnet on the checkerboard lattice

Sylvain Capponi

Published Jan 18, 2017• 16 citations

arXiv HTML PDF

Abstract

We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaus for

m=0, 1/4, 1/2

, and

3/4

, where

m

is the magnetization normalized by its saturation value. These incompressible states correspond to somewhat similar valence-bond crystal phases that break lattice symmetries, though they are different from the already established plaquette phase for

m=0

. Our results are based on exact diagonalization as well as density-matrix renormalization-group large-scale simulations and interpreted in terms of simple parameter-free trial wave functions.

DOI: 10.1103/physrevb.95.014420

Related papers

Multiple magnetization plateaus and magnetic structures in the S = 1 2 Heisenberg model on the checkerboard lattice

Katsuhiro Morita, Naokazu Shibata

We study the ground state of the $S=\frac{1}{2}$ Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group method with the sine-square deformation. We obtain magnetization plateaus at $M/{M}_{\mathrm{sat}}=0,\frac{1}{4},\frac{3}{8},\frac{1}{2}$ , and $\frac{3}{4}$ , where ${M}_{\mathrm{sat}}$ is the saturated magnetization. The obtained $\frac{3}{4}$ plateau state is consistent with the exact result, and the $\frac{1}{2}$ plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the $\frac{1}{3}$ plateau of the kagome lattice. Different four-spin loop structures are obtained in the $\frac{1}{4}$ and $\frac{3}{8}$ plateaus but no corresponding states exist in the kagome lattice. The $\frac{3}{8}$ plateau has a unique magnetic structure of three types of four-spin local quantum states in a $4\sqrt{2}\ifmmode\times\else\texttimes\fi{}2\sqrt{2}$ magnetic unit cell with a 16-fold degeneracy.We study the ground state of the $S=\frac{1}{2}$ Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group method with the sine-square deformation. We obtain magnetization plateaus at $M/{M}_{\mathrm{sat}}=0,\frac{1}{4},\frac{3}{8},\frac{1}{2}$, and $\frac{3}{4}$, where ${M}_{\mathrm{sat}}$ is the saturated magnetization. The obtained $\frac{3}{4}$ plateau state is consistent with the exact result, and the $\frac{1}{2}$ plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the $\frac{1}{3}$ plateau of the kagome lattice. Different four-spin loop structures are obtained in the $\frac{1}{4}$ and $\frac{3}{8}$ plateaus but no corresponding states exist in the kagome lattice. The $\frac{3}{8}$ plateau has a unique magnetic structure of three types of four-spin local quantum states in a $4\sqrt{2}\ifmmode\times\else\texttimes\fi{}2\sqrt{2}$ magnetic unit cell with a 16-fold degeneracy.

arXiv:1608.08327Physical review. B./Physical review. BOct 10, 201615 citations

Numerical study of magnetization plateaus in the spin- 1 2 kagome Heisenberg antiferromagnet

Sylvain Capponi, Oleg Derzhko, A. Honecker +2 more

We clarify the existence of several magnetization plateaus for the kagome $S=\frac{1}{2}$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=\frac{1}{3}$ , $\frac{5}{9}$ , and $\frac{7}{9}$ of the saturation value. These results are confirmed using large-scale exact diagonalization on lattices up to 63 sites.We clarify the existence of several magnetization plateaus for the kagome $S=\frac{1}{2}$ antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site $m=\frac{1}{3}$, $\frac{5}{9}$, and $\frac{7}{9}$ of the saturation value. These results are confirmed using large-scale exact diagonalization on lattices up to 63 sites.

arXiv:1307.0975Physical Review BOct 18, 2013122 citations

Néel and valence-bond crystal phases of frustrated two-dimensional Heisenberg models

S. Moukouri

I use an improved version of the two-step density-matrix renormalization group method to study ground-state properties of the two-dimensional (2D) Heisenberg model on the checkerboard lattice. In this version, the Hamiltonian is projected on a tensor product of two-leg ladders instead of chains. This allows investigations of 2D isotropic models. I show that this method can describe both the magnetically disordered and ordered phases. The ground-state phases of the checkerboard model as ${J}_{2}$ increases are (i) N\'eel with $Q=(\ensuremath{\pi},\ensuremath{\pi})$, (ii) a valence-bond crystal (VBC) of plaquettes, (iii) N\'eel with $Q=(\ensuremath{\pi}∕2,\ensuremath{\pi})$, and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point ${J}_{2}={J}_{1}$ , the ground state is made of weakly interacting plaquettes with a large gap $\ensuremath{\Delta}\ensuremath{\approx}0.67{J}_{1}$ to triplet excitations. The same approach is also applied to the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model. There is no evidence of a columnar dimer phase in the highly frustrated regime.I use an improved version of the two-step density-matrix renormalization group method to study ground-state properties of the two-dimensional (2D) Heisenberg model on the checkerboard lattice. In this version, the Hamiltonian is projected on a tensor product of two-leg ladders instead of chains. This allows investigations of 2D isotropic models. I show that this method can describe both the magnetically disordered and ordered phases. The ground-state phases of the checkerboard model as ${J}_{2}$ increases are (i) N\'eel with $Q=(\ensuremath{\pi},\ensuremath{\pi})$, (ii) a valence-bond crystal (VBC) of plaquettes, (iii) N\'eel with $Q=(\ensuremath{\pi}∕2,\ensuremath{\pi})$, and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point ${J}_{2}={J}_{1}$, the ground state is made of weakly interacting plaquettes with a large gap $\ensuremath{\Delta}\ensuremath{\approx}0.67{J}_{1}$ to triplet excitations. The same approach is also applied to the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model. There is no evidence of a columnar dimer phase in the highly frustrated regime.

Physical Review BFeb 28, 200817 citations

Néel and Valence-Bond Crystal phases of the Two-Dimensional Heisenberg Model on the Checkerboard Lattice

S. Moukouri

I use an improved version of the two-step density matrix renormalization group method to study ground-state properties of the 2D Heisenberg model on the checkerboard lattice. In this version the Hamiltonian is projected on a tensor product of two-leg ladders instead of chains. This allows investigations of 2D isotropic models. I show that this method can describe both the magnetically disordered and ordered phases. The ground-state phases of the checkerboard model as $J_2$ increases are: (i) Néel with $Q=(π,π)$ , (ii) a valence bond crystal (VBC) of plaquettes, (iii) Néel with $Q=(π/2,π)$ , and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point $J_2=J_1$ , the ground state is made of weakly interacting plaquettes with a large gap $Δ\approx 0.67 J_1$ to triplet excitations.I use an improved version of the two-step density matrix renormalization group method to study ground-state properties of the 2D Heisenberg model on the checkerboard lattice. In this version the Hamiltonian is projected on a tensor product of two-leg ladders instead of chains. This allows investigations of 2D isotropic models. I show that this method can describe both the magnetically disordered and ordered phases. The ground-state phases of the checkerboard model as $J_2$ increases are: (i) Néel with $Q=(π,π)$, (ii) a valence bond crystal (VBC) of plaquettes, (iii) Néel with $Q=(π/2,π)$, and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point $J_2=J_1$, the ground state is made of weakly interacting plaquettes with a large gap $Δ\approx 0.67 J_1$ to triplet excitations.

arXiv:0709.2688Sep 17, 20070 citations

Variational study of the magnetization plateaus in the spin- 1 2 kagome Heisenberg antiferromagnet: An approach from vision transformer neural quantum states

Andreas Raikos, Sylvain Capponi, Fabien Alet

We analyze the magnetization curve of the spin-1/2 kagome Heisenberg model in a magnetic field. Using state-of-the-art variational wave functions based on neural networks, we confirm the presence of robust magnetization plateaus at $m=1/3$ , $5/9$ and $7/9$ of the saturation value, stabilized by a spontaneous symmetry breaking of lattice translations with a $\sqrt{3}\times \sqrt{3}$ unit cell. Regarding the more challenging $m=1/9$ plateau, we find two competing valence bond crystals depending on the system size, both breaking translation as well as point group symmetries and with a larger $3\times 3$ unit cell. Such quantum states with local modulations of the magnetization average values could be observed experimentally in the near future.We analyze the magnetization curve of the spin-1/2 kagome Heisenberg model in a magnetic field. Using state-of-the-art variational wave functions based on neural networks, we confirm the presence of robust magnetization plateaus at $m=1/3$, $5/9$ and $7/9$ of the saturation value, stabilized by a spontaneous symmetry breaking of lattice translations with a $\sqrt{3}\times \sqrt{3}$ unit cell. Regarding the more challenging $m=1/9$ plateau, we find two competing valence bond crystals depending on the system size, both breaking translation as well as point group symmetries and with a larger $3\times 3$ unit cell. Such quantum states with local modulations of the magnetization average values could be observed experimentally in the near future.

arXiv:2602.12998Physical review. B./Physical review. BJun 17, 20260 citations

Magnetization plateaus in the spin- 12 antiferromagnetic Heisenberg model on a kagome-strip chain

Katsuhiro Morita, Takanori Sugimoto, Shigetoshi Sota +1 more

The spin- $\frac{1}{2}$ Heisenberg model on a kagome lattice is a typical frustrated quantum spin system. The basic structure of a kagome lattice is also present in the kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin- $\frac{1}{2}$ Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions using the density-matrix renormalization-group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking translational and/or reflection symmetry spontaneously. The structures are classified by an array of five-site unit cells with specific bond-spin correlations. In a case with a nontrivial plateau, namely a 3/10 plateau, we find long-period magnetic structure with a period of four unit cells.The spin-$\frac{1}{2}$ Heisenberg model on a kagome lattice is a typical frustrated quantum spin system. The basic structure of a kagome lattice is also present in the kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-$\frac{1}{2}$ Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions using the density-matrix renormalization-group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking translational and/or reflection symmetry spontaneously. The structures are classified by an array of five-site unit cells with specific bond-spin correlations. In a case with a nontrivial plateau, namely a 3/10 plateau, we find long-period magnetic structure with a period of four unit cells.

arXiv:1710.00508Physical review. B./Physical review. BJan 16, 201818 citations

We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaus for

m=0, 1/4, 1/2

, and

3/4

, where

m

m=0

. Our results are based on exact diagonalization as well as density-matrix renormalization-group large-scale simulations and interpreted in terms of simple parameter-free trial wave functions.

We study the ground state of the

S=\frac{1}{2}

Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group method with the sine-square deformation. We obtain magnetization plateaus at

M/{M}_{\mathrm{sat}}=0,\frac{1}{4},\frac{3}{8},\frac{1}{2}

, and

\frac{3}{4}

, where

{M}_{\mathrm{sat}}

is the saturated magnetization. The obtained

\frac{3}{4}

plateau state is consistent with the exact result, and the

\frac{1}{2}

plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the

\frac{1}{3}

plateau of the kagome lattice. Different four-spin loop structures are obtained in the

\frac{1}{4}

and

\frac{3}{8}

plateaus but no corresponding states exist in the kagome lattice. The

\frac{3}{8}

plateau has a unique magnetic structure of three types of four-spin local quantum states in a $4\sqrt{2}\ifmmode\times\else\texttimes\fi{}2\sqrt{2}$ magnetic unit cell with a 16-fold degeneracy.

We clarify the existence of several magnetization plateaus for the kagome

S=\frac{1}{2}

antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site

m=\frac{1}{3}

\frac{5}{9}

, and

\frac{7}{9}

of the saturation value. These results are confirmed using large-scale exact diagonalization on lattices up to 63 sites.

{J}_{2}

increases are (i) N\'eel with $Q=(\ensuremath{\pi},\ensuremath{\pi})$, (ii) a valence-bond crystal (VBC) of plaquettes, (iii) N\'eel with $Q=(\ensuremath{\pi}∕2,\ensuremath{\pi})$, and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point

{J}_{2}={J}_{1}

, the ground state is made of weakly interacting plaquettes with a large gap $\ensuremath{\Delta}\ensuremath{\approx}0.67{J}_{1}$ to triplet excitations. The same approach is also applied to the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model. There is no evidence of a columnar dimer phase in the highly frustrated regime.

J_2

increases are: (i) Néel with

Q=(π,π)

, (ii) a valence bond crystal (VBC) of plaquettes, (iii) Néel with

Q=(π/2,π)

, and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point

J_2=J_1

, the ground state is made of weakly interacting plaquettes with a large gap

Δ\approx 0.67 J_1

to triplet excitations.

m=1/3

5/9

and

7/9

of the saturation value, stabilized by a spontaneous symmetry breaking of lattice translations with a

\sqrt{3}\times \sqrt{3}

unit cell. Regarding the more challenging

m=1/9

plateau, we find two competing valence bond crystals depending on the system size, both breaking translation as well as point group symmetries and with a larger

3\times 3

unit cell. Such quantum states with local modulations of the magnetization average values could be observed experimentally in the near future.

The spin-

\frac{1}{2}

Heisenberg model on a kagome lattice is a typical frustrated quantum spin system. The basic structure of a kagome lattice is also present in the kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-

\frac{1}{2}

Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions using the density-matrix renormalization-group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking translational and/or reflection symmetry spontaneously. The structures are classified by an array of five-site unit cells with specific bond-spin correlations. In a case with a nontrivial plateau, namely a 3/10 plateau, we find long-period magnetic structure with a period of four unit cells.